Physics. — ''(hl the shape of small drops and (/as-baf)bles'\ By 

 J. E. Verschakfklt. Supplement N". 42f to Uie Commniiicatioiis 

 from the Physical Laboratory at Leiden. (Communicated by 

 Piof. H. Kamkrt,ingh Onnes). 



(Goramunicated in tlie meeting of June 29, 1918). 



§ 1. It is well known that the meridian-section of a liquid drop 

 or gas-bnbble (which we shall suppose to be bodies of revolution) 

 cannot be represented by a tinite equation by means of known 



functions. The differential equation 

 to the section 



1 



i_L// 4?y 



R^ .vdw\\/Y^.y'^ 



k{h-{yy){l) 



has as a first integral the e(|uation 



X sin ff) z=z ^ khx* \ u. 



(2) 



Fig. \. 



where (p represents the angle which 

 the tangent forms with the ^-axis 

 (fig. 1; OF is the axis of revolution) 



andif=:2jr ixydx*), but the computation of u and consequently 



M In this equation k stands for the expressiou — ' ' — , cr being the surface 



fi 



tension, ^j — ^o the difference of the densities below and above the surface in its 



top, g the acceleration of gravity; k is therefore positive or negative according as 



the liquid is below the top of the surface, as with a drop resting on a plane, or 



above it, as with a hanging drop; y is the height of a point of the surface above 



2 

 the tangent plane at the top. h is determined by kh = -— -, i^,, being the radius 



R, 



of curvature at the top ; Rq will be reckoned as positive when the surface is 



hollow upwards, negative in the opposite case. 



') u is evidently the volume of the body which is originated by rotation of the 



surface OAA'O (fig. 1) about the //-axis. Equation (2) may be written in the form 



2:x.vo sin (f = (n^ — ^j)g {nx*h-{-u), (3) 



